STABILITY OF CAUCHY ADDITIVE FUNCTIONAL EQUATION IN A LATTICE RANDOM NORMED SPACE

Abstract

This study investigates the stability of the Cauchy additive functional equation

in lattice random normed spaces (LRN-S). Using lattice structure and random norm techniques, it is shown that any approximate solution under random perturbations is close toa true linear function. The results extend the classical Hyers-Ulam stability concept touncertain and lattice-structured environments.